After squash has been roasting 40 minute, bring broth to a simmer and keep at a bare simmer, covered. Meanwhile, cook onion in butter in a 4 quart pot over moderate heat, stirring until softened, about 6 minutes.

Continue simmering adding broth 1/2 cup at a time, stirring constantly and letting each addition be absorbed before adding the next, until rice is creamy looking, but still al dente(it should have the consistency of thick soup), about 18 minutes total. (There will be leftover broth).

Stir in squash pieces, and then stir in cheese, sage and arugula and simmer, stirring for 1 minute.